IN JNJLTSI INFimTORVM. p^ 



E X E M P L V M. 



12. Inuemre curumn algebraicam, cuius quadra^ 

 tura indefinita pendeat a quadratura circuli , cuius ^er(f 

 area abjcijjae .r — rt rejpondens algebraice exhibeatur. 



Vt qiiadratura curiiae .indefinita a quadratura cir- 

 culi pendeat, ponatur u — V {ifx—xx^^ et \t pofito 

 x:^a fiat z — x^ fiat Sn: «(<? — .t), vt fit z—X-\-na 

 — nx-^zna— n~\)x. Ergo ob i;— V^s/s — 5:5; erit 

 i'— y ( 2 naj- 2 ( « — 1 )Jx—n n a a-^ in{n—i)ax-{n—i )\vx) 

 Ponatur, vt haec formula funplicior euadat, Cijzzna^ 

 critque v zzV (n[n—i)ax-(n--i)''xx)y et ob dz~—(ji—i)dx 

 habebitur Q_— y'(«^.v-.v.v)-f-(«— 1 )V(n[n—\)ax—{n-- 1 ^xx) 

 ac pro curua erit 



^zrjj + y(«^A."-vA)+(«-i)y («(«-i)tf.v-(«-i)'A"x), 



area vero erit 



Jydx—V-\-JdxV{nax-xx)-\-(n-i )JdxV{n{n-i )ax-{n- 1 yxx). 

 Verum hic notandum eft, quemadmodum integrale Judx 

 ita capi ponitur, \t euanefcat pofito xz:l.o, ita quoque 

 integrale Jvdz ita capi debere, vt euanefcat pofito z~o: 

 Qiiamobrem vt tota area euanefcat pofito x — o^ ne- 

 cefle ert, vt quoque fiat z~o hoc cafu ; alioquin enim 

 expreffio areae Jydx complederetur quantitatem con- 

 ftantem portionfm areae circulnris denotantem, quae ca- 

 fu x~a dertrueretur. Hnic autem incommodo occur- 

 retur, fi pro S eiusmodi fumatur funclio, quae pofito xzr^o 



cunnefcat. Sit ergo S =; ^ («- — .v), et srr a'-4- "^ (^-.v), 



et 1'— y (2/2- 2;^), atque quaefito fatisfiet modo folito. 



Pqnatur , vt exprefifio fiat fimpliciflima « — — i, vt fit 



Tom. Nou.V.Com. N zziz 



